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Description of Multivariable Calculus: Volume of Solid of Revolution

Find the volume of the solid that is bounded above and below by the given surfaces z = z_1(x, y) and z = z_2(x, y) and lies above the plane region R bounded by the given curve r = g(u): z = 0, z = 3 + x + y; r = 2 sin u

Solution Preview

I think u here is the same as theta. In that case, we solve it like this:

We define
x=rcos(theta)
y=rsin(theta)
z=r
then the Jacobian would be r. We must find

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Solution Summary

The volume of a solid of revolution is calculated.

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